Learning, post-screening, that “The LEGO Batman Movie” director Chris McKay cut his stop-motion, pop culture incisors on three-seasons-and-a-movie of “Robot Chicken” feels something like — if you’ll be a peach and pardon the simile — the final piece clicking into place in that pixel-y, scale-model-ish helicopter/racecar/pontoon boat/Millennium Falcon you’ve been coaxing into being from a puddle of disparate, primary-colored, plastic Danish peg-bricks.

That is: It fits. It makes sense. It was always there, formless yet undeniable until it was made explicit and you uttered a sotto-voce “of course!” It’s what Lego Oprah (surely that exists) might call an “Everything is Ahawesome” moment. (Good gravy. No more Lego puns for me.)

It explains, in other words, the palpable kinship in sensibility between the incumbent Bat-comedy and the wryly frenetic Seth Green brainchild, which strobe-lights references both broad and arcane at its adoring viewers with the stamina and breakneck pace of a Gatling gun manned by a circa-’90s Dennis Miller.

In case this sounds like a complaint: It isn’t. For one thing, if “Lego Batman” feels something like kissing cousins with “Chicken,” it feels even more unmistakably and specifically at home (by purposeful design, certainly) with its record-breaking, Chris Pratt fronted forebear, “The Lego Movie” (on which McKay served as editor and animation co-director, among other credits). Fans of the latter, thus, should find much to enjoy here. For another thing, it’s replete with more than enough fond-and-loving nods to Batman’s greatest hits (Burton/Keaton, Nolan/Bale, et al.) and deep cuts (Killer Moth? Gentleman Ghost? CONDIMENT KING?) — as well as to pop culture at large — to satisfy Batman casuals, diehards, and don’t-cares alike.

As the film opens, we’re re(re-re)introduced to our iconic, mildly bell-shaped, adorably Byronic antihero (Arnett): He broods, raps cavalierly at the fourth wall, raps (and beatboxes) and thrashes on electric guitar, and saves the city in a stunning pyrotechnic display of superheroic prowess without so much as breaking a shiny yellow sweat. And: He never takes off the cowl. Figuratively, at least, but pretty much literally, too. At home, he absently microwaves lobster thermidor, pads through cavernous, echo-chamber hallways, gazes wistfully at pictures of his parents when he thinks no one’s looking, and otherwise generally worries manservant/father figure Alfred (voiced by Ralph Fiennes, in apparent and much-appreciated observance of my deeply held personal belief that Ralph Fiennes should be in everything, please), who wants nothing more, in keeping with canon, than for his ward to lighten up and let people into his hermetic, kevlar-insulated world. Enter Richard “Dick” Grayson: uncommonly spry orphan, megawatt-candlepower Pollyanna, recent adoptive-son-via misunderstanding to billionaire Bat-beard Bruce Wayne, and soon-to-be alter ego of pantsless ur-sidekick Robin — limned, in a stroke of mad casting genius, by Michael Cera.

“The Lego Batman Movie” is at its best and most brilliant in these moments of winking, hyperbolic-yet spiritually-reverent adaptation. The characters we know like family, the tentpole relationships that have been hewn in granite for decades, are giddily skewed and exaggerated here, but are also yoked to the thrust and load-bearing theme of the tale: No Batman is a Bat-island. (Or, if you like, a Batcave beneath the surface of a Bat-island.) As did “The Lego Movie,” “Lego Batman” creates fruitful comedic juxtaposition by imagining The World’s Greatest Detective as a whiny, moody, braggy, dim, nigh-pathologically self-absorbed virtual adolescent who happens to be a superhuman athlete and crime-fighting savant.

Wisely, though, the film digs deeper to suggest the roots of this Big-style emotional stunting: Bruce is, in many ways, just a well-muscled kid who misses his parents. Alfred, ever of sage word and furrowed brow, a sea of tough love restrained by propriety and diction, struggles to shepherd his Herculean middle-schooler: In one of the cleverer bits divulged in trailers, he places a parental lock on the Batcomputer. Robin, traditionally conceived as a youthful, bright counterpoint to the “Dark Knight,” is here pushed to 11-and-then-some: He communicates in giddy squeals and effervescent ’80s pop songs and takes the world in guilelessly via Coke-bottle lenses that turn his eyes into saucers.

The most inspired mutation, though, is in Batman’s relationship with Zach Galifianakis’s Joker. Under Lego’s watch, the well-documented “you hate me but you need me,” intertwined-fate, two-sides-of-the-same-coin trope is writ flatly and unapologetically as an “An Officer and a Gentleman”-style “why won’t he let me in” movie romance, to the point that, when it resolves, you almost want Bats carting the Clown Prince off in his arms to the silky-gravelly strains of Jennifer Warnes and Joe Cocker. It’s one of those moves, an idea so simple and immediately, obviously right that you can’t believe you haven’t seen it before, or that you didn’t think of it yourself. Well played.

There were brief moments in which I found myself drifting. The story progresses logically and well, and even drew tears from me at certain points (it gets sweet, and I’m a crier), but “Lego Batman” is so engaging when it’s poking practical, affectionate, self-aware fun at the monolithically established Bat-Universe that I found myself wishing for a companion version of the film that eschewed plot and emotional resonance and cohesion and character growth and just let its writers loose to “Robot Chicken” jokes at me for 106 minutes. Still, McKay and company do an impressive job of weaving the thing into a working, breathing, family-friendly cautionary tale about overcoming pain and fear and letting oneself love and be loved again. (Again: I cried. At “Lego Batman.”)

And again, the writing, concepts, and casting are so smack-your-face fantastic at times (Jenny Slate as Harley Quinn!) and so warmly considerate of its fan base (Billy Dee as Two-Face!) that I’m eager for a second viewing. My viewing partner, an enormous “Lego Movie” fan, didn’t dig this outing as much, and I don’t know that I’d necessarily call it a perfect movie, but there are lots of things about it, particularly as a Bat-fan, that I love and appreciate to an extent that, frankly, I want to hug them and never Lego.